Beside the annihilation rate, the dynamical friction due to dark matter density spike would also be very large. If a star is moving inside a collisionless dark matter background, the star would exert a gravitational force to pull the dark matter particles towards it. Then a concentration of the dark matter particles would locate behind the star and exert a collective gravitational force on the star. This collective gravitational force would slow down the star and the resulting effect is called dynamical friction. The idea of dynamical friction was proposed by Chandrasekhar more than 70 years ago [1]}. However, very surprisingly, the dynamical frictional effect in BH-LMXBs has not been seriously examined in previous studies. Most of the related studies are focusing on the compact binary systems [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. Also, no previous study has realized the possible observable consequence of dark matter density spike surrounding a stellar-mass black hole. In this letter, we will discuss the observed fast orbital decays in the two closest BH-LMXBs with the idea of dynamical friction of dark matter density spike.
